Symbolic rewritten in matlab

alpha=log(r)/t0/(r-1);
beta=r*log(r)/t0/(r-1);

p0=p*(exp(-alpha*t)-exp(-beta*t))/(exp(-alpha*t0)-exp(-beta*t0));
%r=?


%I tried this, plug alpha and beta with the expressions

syms r t p p0 t0

alpha=log(r)/t0/(r-1);
beta=r*log(r)/t0/(r-1);

%p0=p*(exp(-(log(r)/t0/(r-1))*t)-exp(-(r*log(r)/t0/(r-1))*t))/(exp(-(log(r)/t0/(r-1))*t0)-exp(-(r*log(r)/t0/(r-1))*t0));
eqn=(p*(exp(-(log(r)/t0/(r-1))*t)-exp(-(r*log(r)/t0/(r-1))*t))/(exp(-(log(r)/t0/(r-1))*t0)-exp(-(r*log(r)/t0/(r-1))*t0))==p0);

r=solve(eqn,[t, p, p0 t0])

%It doesn't give what I want

Hello, I have a equation, p0= above

I want to rewrite it as r=something

how can I do this in MATLAB or any other website?

[Walter Roberson]

You cannot solve one equation for four variables. You should be trying

solve(eqn, r)

Answer 1

[Star Strider]

An analytic solution is likely not possible, due to the nature of the expression.

The only option is to solve it numerically for ‘r’ given appropriate values for the other variables —

syms p p0 r t0 t 
alpha=log(r)/t0/(r-1);
beta=r*log(r)/t0/(r-1);

Eqn = p0 == p*(exp(-alpha*t)-exp(-beta*t))/(exp(-alpha*t0)-exp(-beta*t0))

Eqn = 

p0fcn = matlabFunction(rhs(Eqn)-p0)

p0fcn = function_handle with value:
    @(p,p0,r,t,t0)-p0-(p.*(exp(-(t.*log(r))./(t0.*(r-1.0)))-exp(-(r.*t.*log(r))./(t0.*(r-1.0)))))./(exp(-(r.*log(r))./(r-1.0))-exp(-log(r)./(r-1.0)))

p  = rand;
p0 = rand;
t  = rand;
t0 = rand;

r = fsolve(@(r)p0fcn(p,p0,r,t,t0), rand)

No solution found.

fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance squared, but the vector of function values
is not near zero as measured by the value of the function tolerance.

r = -0.0174

.